Discretized locally active memristor and application in logarithmic map

Li, Haodong; Li, Chunlai; Du, Jianrong

doi:10.1007/s11071-022-07955-w

Cited by 37 publications

(14 citation statements)

References 69 publications

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“…[37][38][39][40][41][42] Therefore, discrete neuron models are more suitable for simulating large-scale neu-ral networks and conducting general research, such as generating chaotic trajectories, pattern recognition, and analyzing synchronized firing behaviors. [43][44][45][46][47][48][49][50][51] As a result, research on discrete neurons has become a hot topic in recent years. In discrete memristor-coupled neural networks, complex dynamical behaviors have been discovered, including coexisting attractors, [52][53][54][55][56] synchronization transitions, and synchronization coexistence.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Ma 马,

Xiong 熊,

Li 李

et al. 2024

Chinese Phys. B

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Synaptic crosstalk is a prevalent phenomenon among neuronal synapses, playing a crucial role in the transmission of neural signals. Therefore, considering synaptic crosstalk behavior and investigating the dynamical behavior of discrete neural networks is highly necessary. In this paper, we propose a heterogeneous discrete neural network (HDNN) consisting of a three-dimensional KTz discrete neuron and a Chialvo discrete neuron. These two neurons are coupled mutually by two discrete memristors and the synaptic crosstalk is considered. The impact of crosstalk strength on the firing behavior of the HDNN is explored through bifurcation diagrams and Lyapunov exponents. It is observed that the HDNN exhibits different coexisting attractors under varying crosstalk strengths. Furthermore, the influence of different crosstalk strengths on the synchronized firing of the HDNN is investigated, revealing a gradual attainment of phase synchronization between the two discrete neurons as the crosstalk strength decreases.

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Section: Introductionmentioning

confidence: 99%

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Ma 马,

Xiong 熊,

Li 李

et al. 2024

Chinese Phys. B

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“…Their results shows that two m-Rulkov neurons can achieve synchronization only when electrically coupled, but not when chemically coupled. Li et al [36] used discrete locally active memristor to construct a logarithmic map, and the coexisting attractors were observed.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Yan 晏,

Li 李,

Li 李

2024

Chinese Phys. B

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Research on discrete memristor-based neural networks has received much attention. However, current research mainly focuses on memristor–based discrete homogeneous neuron networks, while memristor-coupled discrete heterogeneous neuron networks are rarely reported. In this study, a new four-stable discrete locally active memristor is proposed and its nonvolatile and locally active properties are verified by its power-off plot and DC V-I diagram. Based on two-dimensional discrete Izhikevich neuron and two-dimensional discrete Chialvo neuron, a heterogeneous discrete neuron network is constructed by using the proposed discrete memristor as a coupling synapse connecting the two heterogeneous neurons. Considering the coupling strength as the control parameter, chaotic firing, periodic firing and hyperchaotic firing patterns are revealed. In particular, multiple coexisting firing patterns are observed, which are induced by different initial values of the memristor. Phase synchronization between the two heterogeneous neurons is discussed and it is found that they can achieve perfect synchronous at large coupling strength. Furthermore, the effect of Gaussian white noise on synchronization behaviors is also explored. We demonstrate that the presence of noise not only leads to the transition of firing patterns, but also achieves the phase synchronization between two heterogeneous neurons under low coupling strength.

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“…Recently, researchers have shifted their focus to discrete memristors. Introducing discrete memristors to different maps, it was found that discrete memristive chaotic systems have the advantages of high complexity [49][50][51], coexisting attractors [52][53][54], and offset boosting [55]. Furthermore, Peng et al [56] also studied parameter identification for discrete memristive chaotic maps.…”

Section: Introductionmentioning

confidence: 99%

Multistability and Phase Synchronization of Rulkov Neurons Coupled with a Locally Active Discrete Memristor

et al. 2023

Fractal Fract

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In order to enrich the dynamic behaviors of discrete neuron models and more effectively mimic biological neural networks, this paper proposes a bistable locally active discrete memristor (LADM) model to mimic synapses. We explored the dynamic behaviors of neural networks by introducing the LADM into two identical Rulkov neurons. Based on numerical simulation, the neural network manifested multistability and new firing behaviors under different system parameters and initial values. In addition, the phase synchronization between the neurons was explored. Additionally, it is worth mentioning that the Rulkov neurons showed synchronization transition behavior; that is, anti-phase synchronization changed to in-phase synchronization with the change in the coupling strength. In particular, the anti-phase synchronization of different firing patterns in the neural network was investigated. This can characterize the different firing behaviors of coupled homogeneous neurons in the different functional areas of the brain, which is helpful to understand the formation of functional areas. This paper has a potential research value and lays the foundation for biological neuron experiments and neuron-based engineering applications.

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Discretized locally active memristor and application in logarithmic map

Cited by 37 publications

References 69 publications

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Dynamical behavior of memristor-coupled heterogeneous discrete neural networks with synaptic crosstalk

Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Multistability and Phase Synchronization of Rulkov Neurons Coupled with a Locally Active Discrete Memristor

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